Year 10 - Maths
Problem solving with circle theorems
Circle theorems
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit, pupils will use their developed mathematical reasoning skills to derive and use various circle theorems.
Lesson Summary
You will learn to use your knowledge of circle theorems to solve problems.
Key Notes
- Circle theorems can be used in situations involving circles
- It is not always obvious that a circle theorem can be used
- Sometimes you may wish to add more to a diagram in order to deduce more information
Vocabulary To Learn
- Tangent: A tangent of a circle is a line that intersects the circle exactly once.
- Chord: A chord is any line segment joining two points on the circumference of a circle.
- Perpendicular: Two lines are perpendicular if they meet at right angles.
- Equidistant: Points A and B are equidistant from a third point C if the distance AC is equal to the distance BC.
Common Mistakes To Avoid
- Pupils may not recognise or confuse which circle theorems to apply in a multi-step problem.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Circle theorems can be used in situations involving circles. It is not always obvious that a circle theorem can be used.
2. Use this key word in a maths sentence and explain it clearly. 'Tangent'
A tangent of a circle is a line that intersects the circle exactly once. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils may not recognise or confuse which circle theorems to apply in a multi-step problem. Correction: Encourage pupils to add more to a diagram in order to deduce more information about the problem. Drawing an additional line segment, such chord or radius may a useful first step.
More Lessons In This Unit
- Checking and securing understanding of the parts of a circle Study Guide
- Identifying which circle theorem to use Study Guide
- The alternate segment theorem Study Guide
- The angle at the centre of the circle is twice the angle at any point on the circumference Study Guide
- The angle in a semicircle is a right angle Study Guide
- The angles in the same segment are equal Study Guide
- The opposite angles of a cyclic quadrilateral sum to 180° Study Guide
- The perpendicular from the centre of a circle to a chord bisects the chord Study Guide
- The tangent at any point on a circle is perpendicular to the radius at that point Study Guide
- The tangents from an external point are equal in length Study Guide
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